Now that President Donald Trump's historic meeting with North Korean leader Kim Jong Un has come and gone, his legal team's focus is shifting back toward Special Counsel Robert Mueller. And as Bloomberg reports, Mueller - who is pushing to wrap up the investigation as quickly as possible - is mounting one last push to convince Trump and his legal team to voluntarily sit for an interview. While Mueller has suffered the slings and arrows of Trump's wrath - Trump's allies have hurled vitriol at the special counsel on both twitter and cable news - his determination to interview the president remains unshaken.

So, now the two sides must either find common ground - or gear up for a legal battle that would likely need to be resolved by the Supreme Court.

Now, Mueller is intent on quickly resolving a central issue with Trump’s legal team: whether the president will sit voluntarily for an interview in the probe of Russian election meddling, according to current and former U.S. officials. After months of negotiations, the two sides must find common ground or gear up for an unprecedented legal fight likely to go all the way to the Supreme Court.

"It’s a little bit of a game," said Harry Sandick, a former federal prosecutor who’s now a partner with law firm Patterson Belknap Webb & Tyler. "Mueller could subpoena the president but probably doesn’t want to. He faces some litigation risk. Trump could fight the subpoena, but he also faces a political risk."

During their push to turn public opinion against Mueller, Trump's lawyers, led by Jay Sekulow and Rudy Giuliani, have engaged in selective leaking, including back in early May when they leaked a list of 49 questions purportedly turned. As one lawyer who spoke with Bloomberg pointed out, the ongoing negotiations have turned into "a bit of a game." Others have claimed that the leak was intended to pressure Mueller into killing the interview (of course, we all know how that turned out).

"It’s a little bit of a game," said Harry Sandick, a former federal prosecutor who’s now a partner with law firm Patterson Belknap Webb & Tyler. "Mueller could subpoena the president but probably doesn’t want to. He faces some litigation risk. Trump could fight the subpoena, but he also faces a political risk."

The interview is key to Mueller’s investigation into whether Trump or any of his associates helped Russia interfere in the 2016 U.S. election and whether Trump acted to obstruct the probe, one official said.

Meanwhile, Giuliani claimed late last month that he and Trump have already been rehearsing for an in-person interview with Mueller after the special counsel summarily rejected the Trump legal team's request to conduct some of the interview in a written format.

However, since FBI agents raided Trump attorney Michael Cohen's home, office and hotel room and are reportedly preparing to charge him with a crime, the president has grown increasingly wary of an interview.

One problem for Trump, though, is that if Mueller wins at the Supreme Court, he could compel Trump to sit for a Grand Jury for as long as he wants, and subject Trump to questions on a range of topics without providing any advanced warning.

"I think the Supreme Court will rule in Mueller’s favor, but we don’t really know," Sandick said. "If Mueller wins, he can actually put Trump in the grand jury without his lawyer for as long as he wants and ask about any subject he wants."

Furthermore, if Trump chooses the court battle route, Mueller's probe would encounter further delays, as the ruling likely wouldn't arrive until October at the earliest, after the Court returns from its summer recess. That would mean the investigation likely wouldn't wrap up until late this year - or early next year - at the very earliest. It also would open the Republican Party up to a high degree of political risk, because the Court's final ruling could arrive just before the midterms.

But since the beginning of the probe, the biggest obstacle to a direct interview is Trump. The president's legal team came within a hair's breadth of an agreement back in January. But as Trump got cold feet, his team sent Mueller a 20-page letter arguing that Trump isn't entitled to answer Mueller's questions as they invoked Trump's executive privilege.

Regardless of whether the interview happens, Mueller has told Trump's team that he will prepare a report summarizing his findings that will be turned over to the DOJ and, eventually, Congress. Then it will be up to Congress whether to release the report.